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Taking a Trading System Live
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Taking a Trading System Live

  #101 (permalink)
Market Wizard
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swz168 View Post
I've done a Monte Carlo Simulation with the Data Kevin provided me.

I'm currently building up my own Monte-Carlo-Risk model for trading. Currently, I can only provide the metrics below. As already mentioned , I use the Excel add-on @risk.

The first two simulation have following inputs:

Data: 614 trades
Distribution: Discrete! (I will do a simulation with fitted data distribution another time)
Iterations: 10.000
Initial Capital: 10.000

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Let's have a look at the Standard Risk scenario (Sim 1): It tells: The probability that the Equity will not fall below 10.990 is 5% (after 100 trades done). Or: the probability that the equity will exceed 10.990 is 95%.

The last two lines shows the unexpected risk. 95% is the standard scenario risk. And 99% the stress scenario risk.
I have named it Value at Risk "Drawdown", because I compare it to real drawdown. This figure gives a orientation, when to stop a strategy in real trading (depending on your own risk appetite)

Notice: The calculation is totally different to real draw down calculation! Value at Risk "Drawdown" has a weakness, the the more trades, the smaller the VaR-DD (if strategy shows a positive expectancy). So I have to compare simulations with smaller amount of trades with simulation with higher amount of trades (sim 1 and sim 2).

Simulations with smaller number of trades is absolutely necessary. It gives you more detail about the risk. Because if you have a positive expectancy, naturally the end values of an Monte Carlo simulation will be better with higher number of trades.

Interpretation Example for VaR-DD: The probabilty that the drawdown will fall below 39% is 5%.

The most important figure for me is the VaR-DD. All other metrics is more or less playing with numbers.
@Kevin: I've first done a discrete distribution simulation, so that we can directly compare our figures. Could you do the same simulation with your method with the above inputs, so we can compare?


Thanks for the analysis! I can't see your chart, though.

I ran my simulator to evaluate these statements:

"The probability that the Equity will not fall below 10.990 is 5% (after 100 trades done)."

I assume you mean end equity, not equity at any point during the 100 trades. If so, I got 126 cases with equity below $10,990, out of 2500 runs, which is 5.04%. So, I'd say we agree on that point!


"The probabilty that the drawdown will fall below 39% is 5%."

I assume you mean the max drawdown will be less than 39%. I get 104 cases that have max drawdown 39% or larger, which is 4.2%. That is close, but smaller, than your 5% number. For my purposes at least (realizing that this is not a perfect science), I'd say that is a match.


THANKS AGAIN!!

If you have any questions please send me a Private Message or use the futures.io "Ask Me Anything" thread
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  #102 (permalink)
Market Wizard
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Just to clarify, when I say Monte Carlo is "not a perfect science" I don't mean to disparage it or the results. I just know with all the assumptions that go into it, I can't expect the answers to be exact. So, I put a tolerance band around any results (at least in my head).

So, if Monte Carlo says something has a 50% chance of happening, I assume the "real" number could be anywhere from say 40 to 60%. But it likely won't be 10%, or 90%.

My point is I rely on the answers provided, but I do not expect perfection from them.

If you have any questions please send me a Private Message or use the futures.io "Ask Me Anything" thread
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  #103 (permalink)
Elite Member
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kevinkdog View Post

"The probabilty that the drawdown will fall below 39% is 5%."

Your assumptions are correct. I've corrected my text to: The probabilty that the drawdown is 39% or larger is 5%.

Since my simulation used a discrete distribution, the results shouldn't differ much from yours (otherwise the random function in excel would be a total failure). Good to see that this is the case.

When I have more time, I will do a fitted distribution simulation. The results will depend on how you fit them. This method is good if your strategy doesn't make much trades. Then often, a discrete distribution simulation doesn't give you useful results.

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  #104 (permalink)
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kevinkdog View Post
Just to clarify, when I say Monte Carlo is "not a perfect science" I don't mean to disparage it or the results. I just know with all the assumptions that go into it, I can't expect the answers to be exact. So, I put a tolerance band around any results (at least in my head).

So, if Monte Carlo says something has a 50% chance of happening, I assume the "real" number could be anywhere from say 40 to 60%. But it likely won't be 10%, or 90%.

My point is I rely on the answers provided, but I do not expect perfection from them.


Totally agree. Especially in trading, prediction is very hard. Beside that, it is hard to know, how much curve fitted ones strategy is. So end values (equity) of simulations can be total garbage. That is why I mainly focus on risk metrics if I do monte carlo simulation.

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  #105 (permalink)
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swz168 View Post
Your assumptions are correct. I've corrected my text to: The probabilty that the drawdown is 39% or larger is 5%.

Since my simulation used a discrete distribution, the results shouldn't differ much from yours (otherwise the random function in excel would be a total failure). Good to see that this is the case.

When I have more time, I will do a fitted distribution simulation. The results will depend on how you fit them. This method is good if your strategy doesn't make much trades. Then often, a discrete distribution simulation doesn't give you useful results.


When you do this, could you explain for everyone what exactly the difference is between a "fitted distribution" and "discreet distribution" and maybe the general process to determine the fitted model?

If you have any questions please send me a Private Message or use the futures.io "Ask Me Anything" thread
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  #106 (permalink)
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kevinkdog View Post
When you do this, could you explain for everyone what exactly the difference is between a "fitted distribution" and "discreet distribution" and maybe the general process to determine the fitted model?

A discrete distribution contains a finite number of trades showing the profits or loss. Each trade can be drawn with equal probability. If you have no trade with, for example, 50 USD profit, then a trade with 50 USD profit will never occure in your simulation. (Currently done by you and in my simulation above)

A fitted distribution is derived from the discrete distribution. You are searching a distribution model that best fits your data. In other words, you are making assumptions how your distribution probably looks like. You overlay a distribution model on your data. And based on that distribution model, a 50 USD profit trade could also be drawn with a certain probability, which wasn't possible before. So all profits/loss in between the trades from the discrete distribution data and even bigger wins or loss can be drawn, like in the reality. If your distribution assumptions is good, then your simulation quality will be good, even if you have only a few trades of data.

I will make some screenshots, then it will be more clear.

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  #107 (permalink)
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swz168 View Post
A discrete distribution contains a finite number of trades showing the profits or loss. Each trade can be drawn with equal probability. If you have no trade with, for example, 50 USD profit, then a trade with 50 USD profit will never occure in your simulation. (Currently done by you and in my simulation above)

A fitted distribution is derived from the discrete distribution. You are searching a distribution model that best fits your data. In other words, you are making assumptions how your distribution probably looks like. You overlay a distribution model on your data. And based on that distribution model, a 50 USD profit trade could also be drawn with a certain probability, which wasn't possible before. So all profits/loss in between the trades from the discrete distribution data and even bigger wins or loss can be drawn, like in the reality. If your distribution assumptions is good, then your simulation quality will be good, even if you have only a few trades of data.

I will make some screenshots, then it will be more clear.


Thanks. As you mentioned, the way I do it is simpler than the fitted distribution. It will be very interesting to see the "cost" for that simplicity (ie, less reliable results, etc.).

If you have any questions please send me a Private Message or use the futures.io "Ask Me Anything" thread
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  #108 (permalink)
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Just a word to thank @kevinkdog for having initiated this trade and other futures.io (formerly BMT) fellow members for their high-quality contributions.

I find that this thread is of the utmost interest and really shows a professional view on some key aspects of trading (within the retail world).

Thank again!

Nicolas

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  #109 (permalink)
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kevinkdog View Post
I can't see your chart, though.

Strange, at home I saw without problem the image with the numbers.
I will try to upload again later.

Edit: Updated Post# 99. Hope you can see the table now.


Last edited by swz168; September 4th, 2013 at 10:12 AM.
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  #110 (permalink)
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kevinkdog View Post
Thanks. As you mentioned, the way I do it is simpler than the fitted distribution. It will be very interesting to see the "cost" for that simplicity (ie, less reliable results, etc.).

Since your data includes 614 trades, I don't see any problem using a more "simple" simulation. Beside that we already talked about all the uncertainty and assumptions, so I would say that a simple simulation is good enough for trading purpose, if the data is big enough like in your case.

It would be different, if we have only 50 historical trade. Then I wouldn't do a simple simulation, because the results can be questioned a lot.

The data fitting to a distribution model can be all done with @risk with minimum effort. To see how good a data is fitted to a model, their are several statistical tests (like Kolmogorov?Smirnov test - Wikipedia, the free encyclopedia or Chi-squared test - Wikipedia, the free encyclopedia or Anderson?Darling test - Wikipedia, the free encyclopedia)

I still have to find out, which distribution model and statistical tests for fitting I trust most for trading.

Below you see the distribution for 614 trades and the fitting to logistic distribution:
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And a picture to see how good the fitting quality is (the more similar the red and blue line, the better:
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Now for comparison, I randomly draw 50 trades from your discrete distribution. this is the 50 trades distribution and the fitting:
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As you can see, though I only have 50 trades, the result comes close to simulating with 614 trades. Without the fitting we wouldn't be able to do a serious monte carlo simulation.

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